The midfielder is available from the Clarets this summer after last season's relegation.
The Daily Mail says Everton are in talks with Burnley about a fee for McNeil.
The 22-year-old has two years left on his contract at Turf Moor and Burnley also have the option to extend his deal until 2025.
Everton have wanted McNeil since former manager Rafa Benitez's first days last year.
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